Why was Dhritharastra very happy?

In the 9th verse of chapter 2 of Bhagavad Gita for happiness, Arjuna tells Govinda that he will not fight. On hearing these words from Sanjay, Dhritharastra must have been happy to listen to this. However, Arjuna has become a disciple of Krishna rather than his friend, which will take him to the path of enlightenment. Sanjay knew this and understood that Krishna would convince him to fight the war.